The Theory of Ultrafilters

  • W. Wistar Comfort
  • Stylianos Negrepontis

Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 211)

Table of contents

  1. Front Matter
    Pages I-X
  2. W. Wistar Comfort, Stylianos Negrepontis
    Pages 1-20
  3. W. Wistar Comfort, Stylianos Negrepontis
    Pages 21-60
  4. W. Wistar Comfort, Stylianos Negrepontis
    Pages 61-81
  5. W. Wistar Comfort, Stylianos Negrepontis
    Pages 82-100
  6. W. Wistar Comfort, Stylianos Negrepontis
    Pages 101-115
  7. W. Wistar Comfort, Stylianos Negrepontis
    Pages 116-141
  8. W. Wistar Comfort, Stylianos Negrepontis
    Pages 142-163
  9. W. Wistar Comfort, Stylianos Negrepontis
    Pages 164-203
  10. W. Wistar Comfort, Stylianos Negrepontis
    Pages 204-232
  11. W. Wistar Comfort, Stylianos Negrepontis
    Pages 233-261
  12. W. Wistar Comfort, Stylianos Negrepontis
    Pages 262-285
  13. W. Wistar Comfort, Stylianos Negrepontis
    Pages 286-310
  14. W. Wistar Comfort, Stylianos Negrepontis
    Pages 311-340
  15. W. Wistar Comfort, Stylianos Negrepontis
    Pages 341-380
  16. W. Wistar Comfort, Stylianos Negrepontis
    Pages 381-409
  17. W. Wistar Comfort, Stylianos Negrepontis
    Pages 410-452
  18. Back Matter
    Pages 453-484

About this book

Introduction

An ultrafilter is a truth-value assignment to the family of subsets of a set, and a method of convergence to infinity. From the first (logical) property arises its connection with two-valued logic and model theory; from the second (convergence) property arises its connection with topology and set theory. Both these descriptions of an ultrafilter are connected with compactness. The model-theoretic property finds its expression in the construction of the ultraproduct and the compactness type of theorem of Los (implying the compactness theorem of first-order logic); and the convergence property leads to the process of completion by the adjunction of an ideal element for every ultrafilter-i. e. , to the Stone-Cech com­ pactification process (implying the Tychonoff theorem on the compact­ ness of products). Since these are two ways of describing the same mathematical object, it is reasonable to expect that a study of ultrafilters from these points of view will yield results and methods which can be fruitfully crossbred. This unifying aspect is indeed what we have attempted to emphasize in the present work.

Keywords

Compact space Mathematica Ultrafilter algebra arithmetic compactness duality function logic ordinal set theory theorem topology

Authors and affiliations

  • W. Wistar Comfort
    • 1
  • Stylianos Negrepontis
    • 2
    • 3
  1. 1.Department of MathematicsWesleyan UniversityMiddletownUSA
  2. 2.Department of MathematicsAthens UniversityAthensGreece
  3. 3.Department of MathematicsMcGill UniversityMontréalCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-65780-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 1974
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-65782-5
  • Online ISBN 978-3-642-65780-1
  • Series Print ISSN 0072-7830
  • About this book